New constraints on Gruneisen parameters applications to equations of statefor pressure markers

"Regular" linear relations between shock and particle velocities, u(s) = u( so) + c . u(p), imply a divergence of the Hugoniot pressure pH at a critica l compression V-c/V-o = (c - 1)/c, where the thermal pressure Deltap(th)=(g amma /V).DeltaU(th)=p(H)-p(T) becomes very large with respect to the cold ( isothermal) pressure p(T) at this compression. The Hugoniot relation for th e total internal energy U-H results in this case in the relation gamma (c) = 2(c - 1) for the Gruneisen parameter in this region. Experimental data fo r the zero pressure value gamma (o) and its derivative Gamma (gammao) toget her with theoretical data for the limiting value gamma (infinity) = 2/3, an d the additional experimental value gamma (c) are then used to determine th e thermal (phonon) pressure with the common Mie-Gruneisen assumption.